The easy answer is just measure the stuff you want to show off.
But it'll also depend how you want to show them... if you want to show them nose on, it will require more depth than if they were angled, which would require more depth than if in side profile, which would require more depth than if in top/overhead view.
This is especially important when considering if you want to display anything else with them... my parents had custom-made bookcases 15" deep which were OK with a few 1/48 models (F-14, F-106, B-17; all on top and overhanging slightly as displayed), speakers, globe and the particular VHS tape storage boxes we had, but looked much too deep with more standard bookcase fare (DVDs and CDs, books (even most coffee table books), photographs, and figurines). (I don't know why my dad ordered that depth... he may have just measured the widest thing he planned on putting there and letting that dictate, or he might have decided that it was necessary to prevent the TV from looking goofy by sticking out too far from the rest of the stuff on the wall, but I kind of got the sense it was inexperience and lack of foresight, and I digress)
For comparison, keep in mind that a F-15 nose-to-tail is about 18" long, and an F-14 is about 22" if memory serves.
Most people here who look for displays online end up with a good case of sticker shock. Having never bought one, I can't recommend anybody in particular. However, I would recommend broadening your search to include kitchen cabinets (i.e. with the glass doors), trophy cases and industrial display equipment (i.e. for jewelry and small-electronics), and also look around for these items used to save some money, and also consider
IKEA (unfortunately, most of their stuff can't be purchased online; make sure you check the composition of the materials)